Det Ch Insp Wayne Jolley said: “While we have made an arrest, we still need anyone who witnessed the incident or has information to come forward. No detail is too small.”
Jolley, who is leading the investigation, added: “Our thoughts are with the victim’s family.
“This is a shocking act of violence in the heart of a busy town, and we understand the impact this will have on the local community.”
The Met said homicide detectives were leading the investigation and the force was not looking for anyone else in connection with the stabbing.